Question
Answer
$$(a-b)(a^2-5ab+2)=a^3-6a^2b+5ab^2+2a-2b$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a-b)(a^2-5ab+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}a^3-5a^2b+2a-a^2b+5ab^2-2b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^3-6a^2b+5ab^2+2a-2b\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a-b}\right) $ by each term in $ \left( a^2-5ab+2\right) $. $$ \left( \color{blue}{a-b}\right) \cdot \left( a^2-5ab+2\right) = a^3-5a^2b+2a-a^2b+5ab^2-2b $$ |
| ② | Combine like terms: $$ a^3 \color{blue}{-5a^2b} +2a \color{blue}{-a^2b} +5ab^2-2b = a^3 \color{blue}{-6a^2b} +5ab^2+2a-2b $$ |
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